Construction of Bases for the Group of Cyclotomic Units Original Research Article

Subject of investigation is the construction of a basis Bn for the group of cyclotomic units of the nth cyclotomic field. These bases have the property that Bdsubset of or equal toBn for d mid n. For this purpose the notion of weak σ-bases of a module with an involution operating on it is introduced. The weak σ-basis of a special module then leads via explicit given isomorphisms to the desired bases for the group of cyclotomic units.